squiggle.c/extra.c

#include <float.h>
#include <limits.h>
#include <math.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <sys/types.h>
#include <time.h>

// Some error niceties; these won't be used until later
#define MAX_ERROR_LENGTH 500
#define EXIT_ON_ERROR 0
#define PROCESS_ERROR(error_msg) process_error(error_msg, EXIT_ON_ERROR, __FILE__, __LINE__)

// # More cool stuff
// This is no longer necessary to do basic estimation,
// but is still cool

// ## Sample from an arbitrary cdf
struct box {
    int empty;
    double content;
    char* error_msg;
};

struct box process_error(const char* error_msg, int should_exit, char* file, int line)
{
    if (should_exit) {
        printf("@, in %s (%d)", file, line);
        exit(1);
    } else {
        char error_msg[MAX_ERROR_LENGTH];
        snprintf(error_msg, MAX_ERROR_LENGTH, "@, in %s (%d)", file, line); // NOLINT: We are being carefull here by considering MAX_ERROR_LENGTH explicitly.
        struct box error = { .empty = 1, .error_msg = error_msg };
        return error;
    }
}

// Inverse cdf at point
// Two versions of this function:
//   - raw, dealing with cdfs that return doubles
//     - input: cdf: double => double, p
//     - output: Box(number|error)
//   - box, dealing with cdfs that return a box.
//     - input: cdf: double => Box(number|error), p
//     - output: Box(number|error)
struct box inverse_cdf_double(double cdf(double), double p)
{
    // given a cdf: [-Inf, Inf] => [0,1]
    // returns a box with either
    // x such that cdf(x) = p
    // or an error
    // if EXIT_ON_ERROR is set to 1, it exits instead of providing an error

    double low = -1.0;
    double high = 1.0;

    // 1. Make sure that cdf(low) < p < cdf(high)
    int interval_found = 0;
    while ((!interval_found) && (low > -FLT_MAX / 4) && (high < FLT_MAX / 4)) {
        // ^ Using FLT_MIN and FLT_MAX is overkill
        // but it's also the *correct* thing to do.

        int low_condition = (cdf(low) < p);
        int high_condition = (p < cdf(high));
        if (low_condition && high_condition) {
            interval_found = 1;
        } else if (!low_condition) {
            low = low * 2;
        } else if (!high_condition) {
            high = high * 2;
        }
    }

    if (!interval_found) {
        return PROCESS_ERROR("Interval containing the target value not found, in function inverse_cdf");
    } else {

        int convergence_condition = 0;
        int count = 0;
        while (!convergence_condition && (count < (INT_MAX / 2))) {
            double mid = (high + low) / 2;
            int mid_not_new = (mid == low) || (mid == high);
            // double width = high - low;
            // if ((width < 1e-8) || mid_not_new){
            if (mid_not_new) {
                convergence_condition = 1;
            } else {
                double mid_sign = cdf(mid) - p;
                if (mid_sign < 0) {
                    low = mid;
                } else if (mid_sign > 0) {
                    high = mid;
                } else if (mid_sign == 0) {
                    low = mid;
                    high = mid;
                }
            }
        }

        if (convergence_condition) {
            struct box result = { .empty = 0, .content = low };
            return result;
        } else {
            return PROCESS_ERROR("Search process did not converge, in function inverse_cdf");
        }
    }
}

struct box inverse_cdf_box(struct box cdf_box(double), double p)
{
    // given a cdf: [-Inf, Inf] => Box([0,1])
    // returns a box with either
    // x such that cdf(x) = p
    // or an error
    // if EXIT_ON_ERROR is set to 1, it exits instead of providing an error

    double low = -1.0;
    double high = 1.0;

    // 1. Make sure that cdf(low) < p < cdf(high)
    int interval_found = 0;
    while ((!interval_found) && (low > -FLT_MAX / 4) && (high < FLT_MAX / 4)) {
        // ^ Using FLT_MIN and FLT_MAX is overkill
        // but it's also the *correct* thing to do.
        struct box cdf_low = cdf_box(low);
        if (cdf_low.empty) {
            return PROCESS_ERROR(cdf_low.error_msg);
        }

        struct box cdf_high = cdf_box(high);
        if (cdf_high.empty) {
            return PROCESS_ERROR(cdf_low.error_msg);
        }

        int low_condition = (cdf_low.content < p);
        int high_condition = (p < cdf_high.content);
        if (low_condition && high_condition) {
            interval_found = 1;
        } else if (!low_condition) {
            low = low * 2;
        } else if (!high_condition) {
            high = high * 2;
        }
    }

    if (!interval_found) {
        return PROCESS_ERROR("Interval containing the target value not found, in function inverse_cdf");
    } else {

        int convergence_condition = 0;
        int count = 0;
        while (!convergence_condition && (count < (INT_MAX / 2))) {
            double mid = (high + low) / 2;
            int mid_not_new = (mid == low) || (mid == high);
            // double width = high - low;
            if (mid_not_new) {
                // if ((width < 1e-8) || mid_not_new){
                convergence_condition = 1;
            } else {
                struct box cdf_mid = cdf_box(mid);
                if (cdf_mid.empty) {
                    return PROCESS_ERROR(cdf_mid.error_msg);
                }
                double mid_sign = cdf_mid.content - p;
                if (mid_sign < 0) {
                    low = mid;
                } else if (mid_sign > 0) {
                    high = mid;
                } else if (mid_sign == 0) {
                    low = mid;
                    high = mid;
                }
            }
        }

        if (convergence_condition) {
            struct box result = { .empty = 0, .content = low };
            return result;
        } else {
            return PROCESS_ERROR("Search process did not converge, in function inverse_cdf");
        }
    }
}

// Sampler based on inverse cdf and randomness function
struct box sampler_cdf_box(struct box cdf(double), uint64_t* seed)
{
    double p = sample_unit_uniform(seed);
    struct box result = inverse_cdf_box(cdf, p);
    return result;
}
struct box sampler_cdf_double(double cdf(double), uint64_t* seed)
{
    double p = sample_unit_uniform(seed);
    struct box result = inverse_cdf_double(cdf, p);
    return result;
}

/* Could also define other variations, e.g.,
double sampler_danger(struct box cdf(double), uint64_t* seed)
{
    double p = sample_unit_uniform(seed);
    struct box result = inverse_cdf_box(cdf, p);
		if(result.empty){
			exit(1);
		}else{
			return result.content;
		}
}
*/

// Get confidence intervals, given a sampler

typedef struct ci_t {
    float low;
    float high;
} ci;
int compare_doubles(const void* p, const void* q)
{
    // https://wikiless.esmailelbob.xyz/wiki/Qsort?lang=en
    double x = *(const double*)p;
    double y = *(const double*)q;

    /* Avoid return x - y, which can cause undefined behaviour
       because of signed integer overflow. */
    if (x < y)
        return -1; // Return -1 if you want ascending, 1 if you want descending order.
    else if (x > y)
        return 1; // Return 1 if you want ascending, -1 if you want descending order.

    return 0;
}
ci get_90_confidence_interval(double (*sampler)(uint64_t*), uint64_t* seed)
{
    int n = 100 * 1000;
    double* samples_array = malloc(n * sizeof(double));
    for (int i = 0; i < n; i++) {
        samples_array[i] = sampler(seed);
    }
    qsort(samples_array, n, sizeof(double), compare_doubles);

    ci result = {
        .low = samples_array[5000],
        .high = samples_array[94999],
    };
    free(samples_array);

    return result;
}

// # Small algebra manipulations

// here I discover named structs,
// which mean that I don't have to be typing
// struct blah all the time.
typedef struct normal_params_t {
    double mean;
    double std;
} normal_params;

normal_params algebra_sum_normals(normal_params a, normal_params b)
{
    normal_params result = {
        .mean = a.mean + b.mean,
        .std = sqrt((a.std * a.std) + (b.std * b.std)),
    };
    return result;
}

typedef struct lognormal_params_t {
    double logmean;
    double logstd;
} lognormal_params;

lognormal_params algebra_product_lognormals(lognormal_params a, lognormal_params b)
{
    lognormal_params result = {
        .logmean = a.logmean + b.logmean,
        .logstd = sqrt((a.logstd * a.logstd) + (b.logstd * b.logstd)),
    };
    return result;
}

lognormal_params convert_ci_to_lognormal_params(ci x)
{
    double loghigh = logf(x.high);
    double loglow = logf(x.low);
    double logmean = (loghigh + loglow) / 2.0;
    double logstd = (loghigh - loglow) / (2.0 * NORMAL90CONFIDENCE);
    lognormal_params result = { .logmean = logmean, .logstd = logstd };
    return result;
}

ci convert_lognormal_params_to_ci(lognormal_params y)
{
    double h = y.logstd * NORMAL90CONFIDENCE;
    double loghigh = y.logmean + h;
    double loglow = y.logmean - h;
    ci result = { .low = exp(loglow), .high = exp(loghigh) };
    return result;
}